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On June 30 2012 04:54 SimDawg wrote:Show nested quote +On June 30 2012 04:51 JinDesu wrote:http://www.mathrec.org/old/2010jan/solutions.htmlA plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane's speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off? A plane is standing on a runway that can move (some sort of band conveyer). The conveyer belt exactly matches the speed of the wheels at any given time, moving in the opposite direction of rotation. Can the plane take off? It all depends on the wording of the question. As long as the wording of the question does not specifically restrict the translational motion (i.e. conveyer belt exactly matches the speed of the wheels at any given time), then the plane will take off. This is true of the real world - there is no conveyer belt out there that can be made to prevent the plane from taking off. A conveyer belt or treadmill that can keep a plane with frictionless wheels from taking off will require to run to infinite speeds (constant force over time). It doesn't matter if the belt is going 1/2 the speed of the plane, or exactly, or twice. The air over the wings is completely independent of how fast the wheels are moving. Completely. The plane could be moving backward on a conveyor belt and it would still take off.
Again - this is up to the wording of the question. In the real world, there is no conveyer that can keep a plan from taking off. On a completely theoretical treadmill that exactly matches the speed of the wheels at any given time, a plane with wheels of no friction or durability to consider will not be able to take off - there is no translational motion. And given that the plane is producing force (acceleration), the treadmill must also be producing the opposite but equal force translated at the wheel - thus it will eventually reach infinite speeds (as there is no friction).
However, in the real world, there is NO treadmill that can prevent a plane from taking off. The reason why I am bringing up that it is a wording issue is because if the question does not explicitly state that no translational motion can take place, then we can assume that the treadmill has limited powers, the wheels have friction, and things break.
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Aotearoa39261 Posts
On June 30 2012 02:43 mikell wrote:Show nested quote +On June 30 2012 00:13 klicken wrote:
Oh my god, not the airplane again.
Yes it will take off.
This is because the plane accelerates with its engines through the AIR, not with its wheels through the ground.
You could compare it with a very aerodynamical car driving in heavy headwind, since the car accelerates through the ground, and due to its aerodynamical shape is isn't affected much by the wind and thus would drive just fine. ??? the question states that the conveyor belt is moving at the exact same speed as the aeroplanes tyres. the aeroplanes tyres are the only thing propelling the plane forward. the THRUST from the ENGINES are TRANSLATED to the TYRES. if the TYRES are doing ZERO work then the PLANE is not TAKING OFF.LIFT is not generated unless the plane is moving at an appropriate speed. lift is not generated by the engines. the engines serve as a means to propel the plane forward. lift is created from the pressure difference between the top and bottom of the wings. this lift is not generated if the air is not moving over the wings of the plane (which would not be the case if the plane was on a conveyor belt and NOT moving relative to the air). i am not sure why this is so puzzling to some. and that mythbusters episode as above didn't have the conveyor belt moving at the same speed as the plane, if that was the case, the plane would not be moving relative to the observer at any point. This is the bit that is incorrect. The tyres are not propelling the plane forward, it's the engines. If you removed the tyres and placed the plane on a frictionless surface it would be able to take off. Indeed, if tyres propelling the plane were correct then how does a plane fly through air without the tyres propelling it forward? The tyres are just a way for the plane to move while on the ground, and in a way which reduces as much extra drag as possible. Think of it this way, say you were extremely high up in the air (sationary) and dropped a plane from this height. Assuming the plane stays upright (i.e. doesn't begin rotating as it falls), if the plane turns on its engine will it be able to begin flying mid air?
The difficulty in understanding this problem (or maybe why the problem is ill posed) is that plane do not use their tyres to generate forward motion. If they did, they would take off and be unable to sustain their speed with their engines and immediately crash. Thus its impossible for a tyre propelled plane to even fly, let alone take off from a treadmill.
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On June 30 2012 04:58 hzflank wrote:Show nested quote +On June 30 2012 04:56 Phael wrote:On June 30 2012 04:54 hzflank wrote:On June 30 2012 04:51 Phael wrote:
Ok maybe we are talking about two different things.
In that picture, it's implied that the plane stays still on the conveyor belt - where its forward speed is matched by the belt. As in, does not move relative to a person sitting nearby. So if it's moving forward at 100mph, the belt is also running at 100mph, and their speeds cancel out.
If there is no wind blowing, then the plane is also stationary relative to the wind. It's stationary to you, wind is stationary to you, commutative property, etc.
In the mythbuster's scenario, the plane was NOT kept still. It was still moving relative to the viewer, and thus, the wind. So it was able to take off. You are completely missing the point. Because the plane's wheels are free (not powered), no matter how fast the conveyor belt moves, the plan will never be stationary relative to a person standing beside the conveyor belt. The planes engines cause it to accelerate through the air, not over the ground. It will always move forward. This is only true in a frictionless scenario. In the real world (eg. that picture), a conveyor belt moving ANYTHING will exert a force on the object. Hence my original post saying that the plane would catch fire before it was actually stopped.
State 1: both belt and plane at rest.
State 2: plane starts up its engine, belt starts spinning. Forces cancel each other out and plane does not move.
State 3: plane keeps building up thrust, belt keeps spinning faster to apply enough force on the wheels to keep the plane stationary.
State 4: plane applies enough thrust to force the belt to spin so fast something catches on fire. Experiment is nullified.
Until something actually breaks, the plane does not achieve lift-off, how does that not satisfy the question?
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Plane question is pretty stupid, since it's a giant wad of misunderstanding on both sides.
Technically, since we don't have frictionless wheels, it's theoretically possible for a treadmill to move so fast that the miniscule friction of the wheels exactly matches the force of the engines. Of course we're talking something like a treadmill moving at c or something. I don't even know if that'll be enough..
Someone should calculate how fast a treadmill has to move given typical friction of the wheels and typical thrust of the engines. Of course we'd have to assume indestructible wheels.
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Because a standard plane would take off long before the friction caused it to catch fire.
State 1: both belt and plane at rest
State 2: plane starts up its engine, belt starts spinning. The plane begins to move forward because the force causing it to move forward have nothing to do with it's wheels, and the small amount of friction generated is not enough to stop it.
State 3: Plane is in the air long before the friction generated enough heat to cause a problem.
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On June 30 2012 04:59 JinDesu wrote:Show nested quote +On June 30 2012 04:54 SimDawg wrote:On June 30 2012 04:51 JinDesu wrote:http://www.mathrec.org/old/2010jan/solutions.htmlA plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane's speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off? A plane is standing on a runway that can move (some sort of band conveyer). The conveyer belt exactly matches the speed of the wheels at any given time, moving in the opposite direction of rotation. Can the plane take off? It all depends on the wording of the question. As long as the wording of the question does not specifically restrict the translational motion (i.e. conveyer belt exactly matches the speed of the wheels at any given time), then the plane will take off. This is true of the real world - there is no conveyer belt out there that can be made to prevent the plane from taking off. A conveyer belt or treadmill that can keep a plane with frictionless wheels from taking off will require to run to infinite speeds (constant force over time). It doesn't matter if the belt is going 1/2 the speed of the plane, or exactly, or twice. The air over the wings is completely independent of how fast the wheels are moving. Completely. The plane could be moving backward on a conveyor belt and it would still take off. Again - this is up to the wording of the question. In the real world, there is no conveyer that can keep a plan from taking off. On a completely theoretical treadmill that exactly matches the speed of the wheels at any given time, a plane with wheels of no friction or durability to consider will not be able to take off - there is no translational motion. And given that the plane is producing force (acceleration), the treadmill must also be producing the opposite but equal force translated at the wheel - thus it will eventually reach infinite speeds (as there is no friction). However, in the real world, there is NO treadmill that can prevent a plane from taking off. The reason why I am bringing up that it is a wording issue is because if the question does not explicitly state that no translational motion can take place, then we can assume that the treadmill has limited powers, the wheels have friction, and things break.
I get what you're saying now but it's a ridiculous point.
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On June 30 2012 05:09 JeeJee wrote:
Plane question is pretty stupid, since it's a giant wad of misunderstanding on both sides.
Technically, since we don't have frictionless wheels, it's theoretically possible for a treadmill to move so fast that the miniscule friction of the wheels exactly matches the force of the engines. Of course we're talking something like a treadmill moving at c or something. I don't even know if that'll be enough..
Someone should calculate how fast a treadmill has to move given typical friction of the wheels and typical thrust of the engines. Of course we'd have to assume indestructible wheels.
See the link in my post - the calculations are there. It's not "speed" - it's "acceleration".
On June 30 2012 05:10 SimDawg wrote:Show nested quote +On June 30 2012 04:59 JinDesu wrote:On June 30 2012 04:54 SimDawg wrote:On June 30 2012 04:51 JinDesu wrote:http://www.mathrec.org/old/2010jan/solutions.htmlA plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane's speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off? A plane is standing on a runway that can move (some sort of band conveyer). The conveyer belt exactly matches the speed of the wheels at any given time, moving in the opposite direction of rotation. Can the plane take off? It all depends on the wording of the question. As long as the wording of the question does not specifically restrict the translational motion (i.e. conveyer belt exactly matches the speed of the wheels at any given time), then the plane will take off. This is true of the real world - there is no conveyer belt out there that can be made to prevent the plane from taking off. A conveyer belt or treadmill that can keep a plane with frictionless wheels from taking off will require to run to infinite speeds (constant force over time). It doesn't matter if the belt is going 1/2 the speed of the plane, or exactly, or twice. The air over the wings is completely independent of how fast the wheels are moving. Completely. The plane could be moving backward on a conveyor belt and it would still take off. Again - this is up to the wording of the question. In the real world, there is no conveyer that can keep a plan from taking off. On a completely theoretical treadmill that exactly matches the speed of the wheels at any given time, a plane with wheels of no friction or durability to consider will not be able to take off - there is no translational motion. And given that the plane is producing force (acceleration), the treadmill must also be producing the opposite but equal force translated at the wheel - thus it will eventually reach infinite speeds (as there is no friction). However, in the real world, there is NO treadmill that can prevent a plane from taking off. The reason why I am bringing up that it is a wording issue is because if the question does not explicitly state that no translational motion can take place, then we can assume that the treadmill has limited powers, the wheels have friction, and things break. I get what you're saying now but it's a ridiculous point.
I don't see why it's a ridiculous point - the answer to the original post
"If a plane was on a conveyor belt, trying to take off, but the conveyor belt would match the speed of the planes wheels PERFECTLY in the opposite direction, would the plane ever take off?"
Is a solid No because it restricts the translational motion of the plane. However, the other correct answer is (and some posters mention this) "The plane cannot lift off unless the treadmill/wheel/bearing/etc breaks".
The statement "The airplane will lift off regardless" does not keep to the wording of the question. If you play with riddles and not keep to the wording of the question, then you are not playing correctly at all.
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On June 30 2012 05:10 hzflank wrote:
State 2: plane starts up its engine, belt starts spinning. The plane begins to move forward because the force causing it to move forward have nothing to do with it's wheels, and the small amount of friction generated is not enough to stop it.
Why does this happen?
see: http://webphysics.davidson.edu/faculty/dmb/py430/friction/rolling.html
Yes, the wheels rolling over the treadmill will cause a backwards force. If the treadmill spins fast enough, this force cancels out the forward thrust of the plane's engines.
And it's not a "small" amount of friction. Since the wheels on belt situation is rubber on rubber, I'd guesstimate that the Crr is roughly 0.03, so the belt only has to spin at about 30 times the speed of what the plane would be moving at (so, in this case, if the plane needs 100 mph to take off and applies the thrust necessary to reach 100mph on the ground, the treadmill only has to spin at around 3000 mph - totally possible).
Edit: You must be aware of this if you've ever driven anywhere. When you release the gas pedal, your car decelerates. It decelerates precisely because due to rolling friction. It might not be that strong, but then my car isn't traveling all that fast. If the belt can spin fast enough without breaking, and the wheels don't get burned out, then you can keep the plane stationary.
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On June 30 2012 05:10 JinDesu wrote:Show nested quote +On June 30 2012 05:09 JeeJee wrote:
Plane question is pretty stupid, since it's a giant wad of misunderstanding on both sides.
Technically, since we don't have frictionless wheels, it's theoretically possible for a treadmill to move so fast that the miniscule friction of the wheels exactly matches the force of the engines. Of course we're talking something like a treadmill moving at c or something. I don't even know if that'll be enough..
Someone should calculate how fast a treadmill has to move given typical friction of the wheels and typical thrust of the engines. Of course we'd have to assume indestructible wheels. See the link in my post - the calculations are there. It's not "speed" - it's "acceleration". Show nested quote +On June 30 2012 05:10 SimDawg wrote:On June 30 2012 04:59 JinDesu wrote:On June 30 2012 04:54 SimDawg wrote:On June 30 2012 04:51 JinDesu wrote:http://www.mathrec.org/old/2010jan/solutions.htmlA plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane's speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off? A plane is standing on a runway that can move (some sort of band conveyer). The conveyer belt exactly matches the speed of the wheels at any given time, moving in the opposite direction of rotation. Can the plane take off? It all depends on the wording of the question. As long as the wording of the question does not specifically restrict the translational motion (i.e. conveyer belt exactly matches the speed of the wheels at any given time), then the plane will take off. This is true of the real world - there is no conveyer belt out there that can be made to prevent the plane from taking off. A conveyer belt or treadmill that can keep a plane with frictionless wheels from taking off will require to run to infinite speeds (constant force over time). It doesn't matter if the belt is going 1/2 the speed of the plane, or exactly, or twice. The air over the wings is completely independent of how fast the wheels are moving. Completely. The plane could be moving backward on a conveyor belt and it would still take off. Again - this is up to the wording of the question. In the real world, there is no conveyer that can keep a plan from taking off. On a completely theoretical treadmill that exactly matches the speed of the wheels at any given time, a plane with wheels of no friction or durability to consider will not be able to take off - there is no translational motion. And given that the plane is producing force (acceleration), the treadmill must also be producing the opposite but equal force translated at the wheel - thus it will eventually reach infinite speeds (as there is no friction). However, in the real world, there is NO treadmill that can prevent a plane from taking off. The reason why I am bringing up that it is a wording issue is because if the question does not explicitly state that no translational motion can take place, then we can assume that the treadmill has limited powers, the wheels have friction, and things break. I get what you're saying now but it's a ridiculous point. I don't see why it's a ridiculous point - the answer to the original post Show nested quote +"If a plane was on a conveyor belt, trying to take off, but the conveyor belt would match the speed of the planes wheels PERFECTLY in the opposite direction, would the plane ever take off?" Is a solid No because it restricts the translational motion of the plane. However, the other correct answer is (and some posters mention this) " The plane cannot lift off unless the treadmill/wheel/bearing/etc breaks". The statement " The airplane will lift off regardless" does not keep to the wording of the question. If you play with riddles and not keep to the wording of the question, then you are not playing correctly at all.
Wut, you're back to being wrong again.
The belt matching the speed perfectly doesn't remove the friction from the wheels to the belt. You saying frictionless wheels removes the friction.
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On June 30 2012 05:22 Phael wrote:Show nested quote +On June 30 2012 05:10 hzflank wrote:
State 2: plane starts up its engine, belt starts spinning. The plane begins to move forward because the force causing it to move forward have nothing to do with it's wheels, and the small amount of friction generated is not enough to stop it.
Why does this happen? see: http://webphysics.davidson.edu/faculty/dmb/py430/friction/rolling.htmlYes, the wheels rolling over the treadmill will cause a backwards force. If the treadmill spins fast enough, this force cancels out the forward thrust of the plane's engines. And it's not a "small" amount of friction. Since the wheels on belt situation is rubber on rubber, I'd guesstimate that the Crr is roughly 0.03, so the belt only has to spin at about 30 times the speed of what the plane would be moving at (so, in this case, if the plane needs 100 mph to take off and applies the thrust necessary to reach 100mph on the ground, the treadmill only has to spin at around 3000 mph - totally possible).
It happens because the engine creates a force that causes the plane to accelerate forwards through the air. The engine does not make the wheels turn. The wheels only turn because of friction against the ground. In theory, a plane does not need wheels at all to take off, the wheels just make it easier by massively reducing the friction against the ground.
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Wait, wait, I'm back to thinking my original thought that you're talking math teacher uselessness.
The plane gets its thrust not from the friction between the wheels and the ground but from the engine and the air. It's completely independent of the ground.
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On June 30 2012 05:24 SimDawg wrote:Show nested quote +On June 30 2012 05:10 JinDesu wrote:On June 30 2012 05:09 JeeJee wrote:
Plane question is pretty stupid, since it's a giant wad of misunderstanding on both sides.
Technically, since we don't have frictionless wheels, it's theoretically possible for a treadmill to move so fast that the miniscule friction of the wheels exactly matches the force of the engines. Of course we're talking something like a treadmill moving at c or something. I don't even know if that'll be enough..
Someone should calculate how fast a treadmill has to move given typical friction of the wheels and typical thrust of the engines. Of course we'd have to assume indestructible wheels. See the link in my post - the calculations are there. It's not "speed" - it's "acceleration". On June 30 2012 05:10 SimDawg wrote:On June 30 2012 04:59 JinDesu wrote:On June 30 2012 04:54 SimDawg wrote:On June 30 2012 04:51 JinDesu wrote:http://www.mathrec.org/old/2010jan/solutions.htmlA plane is standing on a runway that can move (some sort of band conveyer). The plane moves in one direction, while the conveyer moves in the opposite direction. This conveyer has a control system that tracks the plane's speed and tunes the speed of the conveyer to be exactly the same (but in the opposite direction). Can the plane take off? A plane is standing on a runway that can move (some sort of band conveyer). The conveyer belt exactly matches the speed of the wheels at any given time, moving in the opposite direction of rotation. Can the plane take off? It all depends on the wording of the question. As long as the wording of the question does not specifically restrict the translational motion (i.e. conveyer belt exactly matches the speed of the wheels at any given time), then the plane will take off. This is true of the real world - there is no conveyer belt out there that can be made to prevent the plane from taking off. A conveyer belt or treadmill that can keep a plane with frictionless wheels from taking off will require to run to infinite speeds (constant force over time). It doesn't matter if the belt is going 1/2 the speed of the plane, or exactly, or twice. The air over the wings is completely independent of how fast the wheels are moving. Completely. The plane could be moving backward on a conveyor belt and it would still take off. Again - this is up to the wording of the question. In the real world, there is no conveyer that can keep a plan from taking off. On a completely theoretical treadmill that exactly matches the speed of the wheels at any given time, a plane with wheels of no friction or durability to consider will not be able to take off - there is no translational motion. And given that the plane is producing force (acceleration), the treadmill must also be producing the opposite but equal force translated at the wheel - thus it will eventually reach infinite speeds (as there is no friction). However, in the real world, there is NO treadmill that can prevent a plane from taking off. The reason why I am bringing up that it is a wording issue is because if the question does not explicitly state that no translational motion can take place, then we can assume that the treadmill has limited powers, the wheels have friction, and things break. I get what you're saying now but it's a ridiculous point. I don't see why it's a ridiculous point - the answer to the original post "If a plane was on a conveyor belt, trying to take off, but the conveyor belt would match the speed of the planes wheels PERFECTLY in the opposite direction, would the plane ever take off?" Is a solid No because it restricts the translational motion of the plane. However, the other correct answer is (and some posters mention this) " The plane cannot lift off unless the treadmill/wheel/bearing/etc breaks". The statement " The airplane will lift off regardless" does not keep to the wording of the question. If you play with riddles and not keep to the wording of the question, then you are not playing correctly at all. Wut, you're back to being wrong again. The belt matching the speed perfectly doesn't remove the friction from the wheels to the belt. You saying frictionless wheels removes the friction.
Wheel bearing friction does not matter in the scenario:
The plane's propeller provides forward thrust. This is balanced by a rearward force from the wheels onto the axles. This rearward force must be provided by the rearward force of the conveyer belt on the wheels at the point of contact. These forces are applied at an offset equal to the wheels' radius. That produces a torque on each wheel, causing the wheel to spin. That is, the torque on the wheels is balanced by the angular acceleration of the wheels. Later, the friction of a non-ideal wheel may increase enough to help balance the torque, but it is negligible at the outset. Note (and this is important) that the forces will balance, and the plane will not take off even if the wheels are frictionless, because the inertia and angular acceleration of the wheels will balance the thrust from the propellers and the force of the conveyer on the wheels.
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On June 30 2012 05:31 hzflank wrote:Show nested quote +On June 30 2012 05:22 Phael wrote:On June 30 2012 05:10 hzflank wrote:
State 2: plane starts up its engine, belt starts spinning. The plane begins to move forward because the force causing it to move forward have nothing to do with it's wheels, and the small amount of friction generated is not enough to stop it.
Why does this happen? see: http://webphysics.davidson.edu/faculty/dmb/py430/friction/rolling.htmlYes, the wheels rolling over the treadmill will cause a backwards force. If the treadmill spins fast enough, this force cancels out the forward thrust of the plane's engines. And it's not a "small" amount of friction. Since the wheels on belt situation is rubber on rubber, I'd guesstimate that the Crr is roughly 0.03, so the belt only has to spin at about 30 times the speed of what the plane would be moving at (so, in this case, if the plane needs 100 mph to take off and applies the thrust necessary to reach 100mph on the ground, the treadmill only has to spin at around 3000 mph - totally possible). It happens because the engine creates a force that causes the plane to accelerate forwards through the air. The engine does not make the wheels turn. The wheels only turn because of friction against the ground. In theory, a plane does not need wheels at all to take off, the wheels just make it easier by massively reducing the friction against the ground.
Are you saying there is NO friction between the wheel and the conveyor belt then? So if the plane was coasting along, and turned off its engine, it would not roll to a stop?
There's always some friction. Magnify that friction with a conveyor belt, and you could get enough friction force to keep the plane stationary.
I don't disagree that the engine provides force. Engine provides F -> thataway.
Conveyor belt spins <- thataway, applying a frictional rolling force on the wheels <- thataway.
Spin the belt and wheels fast enough ... and you'll get a force equal to F <- thataway.
So the plane has a F -> that direction from the engine, and a F <- that direction from the wheels, they cancel each other out and it stays still.
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On June 30 2012 05:02 Phael wrote:Show nested quote +On June 30 2012 04:58 hzflank wrote:On June 30 2012 04:56 Phael wrote:On June 30 2012 04:54 hzflank wrote:On June 30 2012 04:51 Phael wrote:
Ok maybe we are talking about two different things.
In that picture, it's implied that the plane stays still on the conveyor belt - where its forward speed is matched by the belt. As in, does not move relative to a person sitting nearby. So if it's moving forward at 100mph, the belt is also running at 100mph, and their speeds cancel out.
If there is no wind blowing, then the plane is also stationary relative to the wind. It's stationary to you, wind is stationary to you, commutative property, etc.
In the mythbuster's scenario, the plane was NOT kept still. It was still moving relative to the viewer, and thus, the wind. So it was able to take off. You are completely missing the point. Because the plane's wheels are free (not powered), no matter how fast the conveyor belt moves, the plan will never be stationary relative to a person standing beside the conveyor belt. The planes engines cause it to accelerate through the air, not over the ground. It will always move forward. This is only true in a frictionless scenario. In the real world (eg. that picture), a conveyor belt moving ANYTHING will exert a force on the object. Hence my original post saying that the plane would catch fire before it was actually stopped. State 1: both belt and plane at rest. State 2: plane starts up its engine, belt starts spinning. Forces cancel each other out and plane does not move.State 3: plane keeps building up thrust, belt keeps spinning faster to apply enough force on the wheels to keep the plane stationary. State 4: plane applies enough thrust to force the belt to spin so fast something catches on fire. Experiment is nullified. Until something actually breaks, the plane does not achieve lift-off, how does that not satisfy the question?
you've laid out the scenario but missed the point. Nothing says the plane remains stationary. The riddle only says the belt matches the speed of the wheels. You are making that leap in logic, that the belt matching the speed of the wheels forces the plane to stay stationary. Yes, the belt will accelerate faster and faster as the plane begins to move, but since planes do not transfer the force of the engines through the landing gear no force from the belt slows its forward motion (assuming no friction).
As it has been said already, the engines pulling the plane through the air are what allow it to fly. Only the relative airspeed of the wing is important when generating lift, not ground speed.
Put a spin on it: If the plane sits on an accelerating conveyor (assuming no friction) will it it take off? No. The conveyor will accelerate and spin the wheels, but the plane's inertia will keep it in place relative to the air and it will not generate lift.
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On June 30 2012 05:34 Phael wrote:Show nested quote +On June 30 2012 05:31 hzflank wrote:On June 30 2012 05:22 Phael wrote:On June 30 2012 05:10 hzflank wrote:
State 2: plane starts up its engine, belt starts spinning. The plane begins to move forward because the force causing it to move forward have nothing to do with it's wheels, and the small amount of friction generated is not enough to stop it.
Why does this happen? see: http://webphysics.davidson.edu/faculty/dmb/py430/friction/rolling.htmlYes, the wheels rolling over the treadmill will cause a backwards force. If the treadmill spins fast enough, this force cancels out the forward thrust of the plane's engines. And it's not a "small" amount of friction. Since the wheels on belt situation is rubber on rubber, I'd guesstimate that the Crr is roughly 0.03, so the belt only has to spin at about 30 times the speed of what the plane would be moving at (so, in this case, if the plane needs 100 mph to take off and applies the thrust necessary to reach 100mph on the ground, the treadmill only has to spin at around 3000 mph - totally possible). It happens because the engine creates a force that causes the plane to accelerate forwards through the air. The engine does not make the wheels turn. The wheels only turn because of friction against the ground. In theory, a plane does not need wheels at all to take off, the wheels just make it easier by massively reducing the friction against the ground. Are you saying there is NO friction between the wheel and the conveyor belt then? So if the plane was coasting along, and turned off its engine, it would not roll to a stop? There's always some friction. Magnify that friction with a conveyor belt, and you could get enough friction force to keep the plane stationary.
You are stretching it dude. The idea is that the wheels spin freely.
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On June 30 2012 05:36 Ghost151 wrote:Show nested quote +On June 30 2012 05:02 Phael wrote:On June 30 2012 04:58 hzflank wrote:On June 30 2012 04:56 Phael wrote:On June 30 2012 04:54 hzflank wrote:On June 30 2012 04:51 Phael wrote:
Ok maybe we are talking about two different things.
In that picture, it's implied that the plane stays still on the conveyor belt - where its forward speed is matched by the belt. As in, does not move relative to a person sitting nearby. So if it's moving forward at 100mph, the belt is also running at 100mph, and their speeds cancel out.
If there is no wind blowing, then the plane is also stationary relative to the wind. It's stationary to you, wind is stationary to you, commutative property, etc.
In the mythbuster's scenario, the plane was NOT kept still. It was still moving relative to the viewer, and thus, the wind. So it was able to take off. You are completely missing the point. Because the plane's wheels are free (not powered), no matter how fast the conveyor belt moves, the plan will never be stationary relative to a person standing beside the conveyor belt. The planes engines cause it to accelerate through the air, not over the ground. It will always move forward. This is only true in a frictionless scenario. In the real world (eg. that picture), a conveyor belt moving ANYTHING will exert a force on the object. Hence my original post saying that the plane would catch fire before it was actually stopped. State 1: both belt and plane at rest. State 2: plane starts up its engine, belt starts spinning. Forces cancel each other out and plane does not move.State 3: plane keeps building up thrust, belt keeps spinning faster to apply enough force on the wheels to keep the plane stationary. State 4: plane applies enough thrust to force the belt to spin so fast something catches on fire. Experiment is nullified. Until something actually breaks, the plane does not achieve lift-off, how does that not satisfy the question? you've laid out the scenario but missed the point. Nothing says the plane remains stationary. The riddle only says the belt matches the speed of the wheels. You are making that leap in logic, that the belt matching the speed of the wheels forces the plane to stay stationary. Yes, the belt will accelerate faster and faster as the plane begins to move, but since planes do not transfer the force of the engines through the landing gear no force from the belt slows its forward motion (assuming no friction). As it has been said already, the engines pulling the plane through the air are what allow it to fly. Only the relative airspeed of the wing is important when generating lift, not ground speed. Put a spin on it: If the plane sits on an accelerating conveyor (assuming no friction) will it it take off? No. The conveyor will accelerate and spin the wheels, but the plane's inertia will keep it in place relative to the air and it will not generate lift.
If the plane does not move relative to the conveyor belt, then the wheels and belt are spinning at the exact same speed whether it's .5mph or 500000 mph.
Furthermore, the only scenario in which the belt and wheel move at the same speed is IF the plane is stationary. If there is any discrepancy in their speed, the plane is moving, which fails the premise of the riddle and obviously allows it to lift-off.
You are stretching it dude. The idea is that the wheels spin freely.
How is applying something that is ever-present stretching it? Spinning freely only ever occurs in frictionless -ie made up - scenarios.
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On June 30 2012 05:32 SimDawg wrote:
Wait, wait, I'm back to thinking my original thought that you're talking math teacher uselessness.
The plane gets its thrust not from the friction between the wheels and the ground but from the engine and the air. It's completely independent of the ground.
This is exactly where you are misreading the question.
If the wheel is touching the treadmill, and the wheel spinning forwards at a certain speed due to the propulsion from the aircraft - and the treadmill is moving backwards at the exact same speed as the wheel, then there cannot be any forward motion. That's how the question is phrased.
You are much better off arguing that the question is phrased in such a way that cannot exist in the real world.
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The treadmill will not be moving at the same speed as the wheels. That is physically impossible because the plane's engine does not provide any power to the wheels. The faster the treadmill moves, the faster the wheels spin and the wheels will always spin faster than the treadmill, unless friction gets sufficiently high to cause the wheels (or treadmill) to break due to the heat being generated.
The treadmill spins at the speed that the plane is moving, not at the speed that the wheels are spinning. Plane speed + treadmill speed = wheel speed, and the question states that the treadmill and the plane move at the same speed. The wheels will always be spinning twice as fast as the plane or treadmill are moving.
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Then that invalidates the original premise of the question, which I quote here:
if a plane was on a conveyor belt, trying to take off, but the conveyor belt would match the speed of the planes wheels PERFECTLY in the opposite direction, would the plane ever take off?
The only way that this condition is satisfied is if the plane is stationary on the treadmill, no other possible scenarios.
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I don't know if you're trolls, stupid or ignorant.
Here i drew you a pic, the only difference with the threadmill is that the wheels will spin twice as fast.
The plane will still MOVE THE SAME SPEED RELATIVE TO THE AIR and thus take off as normal.
![[image loading]](http://i.imgur.com/OGPR8.png)
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EPT
